determine whether the function is even, odd or neither

Question

anonymous · Answer

$$f(x) = x (\sin ^{3}x)$$

ganeshie8 · Answer

start by finding f(-x)
if u get f(-x) = f(x)  then the function is even
if u get f(-x) = -f(x)  then the function is odd
if dont get any of above, then its neither

ganeshie8 · Answer

$f(x) = x (\sin ^{3}x)$

$f(-x) = (-x) (\sin ^{3}(-x))$

simplify

ganeshie8 · Answer

use this :  $\sin(-x) =   -\sin(x)$

anonymous · Answer

so its odd?

ganeshie8 · Answer

$f(x) = x (\sin ^{3}x)$

$f(-x) = (-x) (\sin ^{3}(-x))$

$f(-x) = (-x) (\sin (-x))^3$

$f(-x) = (-x) (-\sin (x))^3$

$f(-x) = (-x) (-1)^3 (\sin^3 (x))$

$f(-x) = (-x) (-1) (\sin^3 (x))$

$f(-x) = x (\sin^3 (x))$

$f(-x) = f(x) $

ganeshie8 · Answer

EVEN !

anonymous · Answer

wow i got confused there but with each step it makes more sense...thank you!

ganeshie8 · Answer

good :)